quant-econ Solutions: The Lucas Asset Pricing Model

In [1]:

    

%matplotlib inline


    

In [2]:

    

from __future__ import division  # Omit for Python 3.x
import numpy as np
import matplotlib.pyplot as plt
from quantecon import AssetPrices


    

In [3]:

    

"""
Authors: David Evans, John Stachurski and Thomas J. Sargent
"""

# == Define primitives == #
n = 5
P = 0.0125 * np.ones((n, n))
P += np.diag(0.95 - 0.0125 * np.ones(5))
s = np.array([1.05, 1.025, 1.0, 0.975, 0.95])
gamma = 2.0
beta = 0.94
zeta = 1.0

ap = AssetPrices(beta, P, s, gamma)

v = ap.tree_price()
print "Lucas Tree Prices: ", v

v_consol = ap.consol_price(zeta)
print "Consol Bond Prices: ", v_consol

P_tilde = P * s**(1-gamma)
temp = beta * P_tilde.dot(v) - beta * P_tilde.dot(np.ones(n))
print "Should be 0: ",  v - temp 

p_s = 150.0
w_bar, w_bars = ap.call_option(zeta, p_s, T = [10,20,30])


    

    




Lucas Tree Prices:  [ 12.28465197  14.42111319  17.45713702  22.11237355  30.15323666]
Consol Bond Prices:  [  75.51427238   98.64225987  140.69501276  240.82930111  786.23683599]
Should be 0:  [ 1.72509033  1.79371484  1.86577057  1.94152147  2.02125926]

In [4]:

    

from quantecon import lucas_tree, compute_lt_price

fig, ax = plt.subplots(figsize=(10,7))

ax.set_xlabel(r'$y$', fontsize=16)
ax.set_ylabel(r'price', fontsize=16)

for beta in (.95, 0.98):
    tree = lucas_tree(gamma=2, beta=beta, alpha=0.90, sigma=0.1)
    grid, price_vals = compute_lt_price(tree)
    label = r'$\beta = {}$'.format(beta)
    ax.plot(grid, price_vals, lw=2, alpha=0.7, label=label)

ax.legend(loc='upper left')
ax.set_xlim(min(grid), max(grid))


    

    




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0.0241528912394






    
Out[4]:





(0.39945149497311855, 2.5034328637756031)






    

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